Method and system for the determination of wind speeds and incident radiation parameters of overhead power lines

ABSTRACT

The present invention relates to a method and system for the determination of parameters related to the speed of wind that blows near an overhead electrical power line (single or bundle conductors). The parameters include an “effective wind speed” as well as an “effective incident radiation” acting on a power line span. The measurement is made by using the combination of mechanical vibrations and movements/positions in two or three dimensions through sensors in direct link with the power line conductor.

FIELD OF THE INVENTION

The present invention relates to a method and system for the determination of parameters related to the speed of wind that blows near an overhead electrical power line (single or bundle conductors). In particular, such parameters include an effective perpendicular wind speed (hereinafter referred to as the “effective wind speed”), which is the speed that would have a wind blowing perpendicularly to the conductor axis and having the same cooling effect on the conductor as the actual wind. In addition, the combination of solar radiation and albedo on power line conductor is hereinafter referred to as the “effective incident radiation”.

BACKGROUND OF THE INVENTION

As explained in U.S. Pat. No. 8,184,015, continuous monitoring of electrical power lines, in particular high-voltage overhead lines, is essential to timely detect anomalous conditions which could lead to a power outage. Measurement of the sag of power lines to determine whether the sag is lower than a maximum value is becoming a mandatory requirement in some countries.

The device and method described in U.S. Pat. No. 8,184,015 can monitor the sag continuously on a power line span, without the need for external data, such as topological data, conductor or span data, weather data, or sagging conditions, which makes the invention unique. The basic principle of that invention is the detection of mechanical dynamic properties of the power lines only based on mechanical frequencies detection from 0 to some tens of Hertz (Hz). Indeed, power lines in the field are always subject to movements and vibrations, which may be very small but detectable by their accelerations in both time and frequency domains.

Such remarkable properties may be used to determine many other features. The new method of the present invention can also be used by other devices equipped with accelerometers.

The ampacity of a conductor is that maximal constant electrical current which will meet the design, security and safety criteria (e.g. electrical clearance) of a particular line on which the conductor is used (see reference 5). The method to evaluate ampacity from data are explained in many books (such as reference 1) and technical brochures from international organizations, such as The International Council on Large Electric Systems (CIGRE) publications (see references 2, 4 and 5), which use weather data as locally measured or simulated following international recommendations as explained, for example, in CIGRE (see reference 3) or The Institute of Electrical and Electronics Engineers (IEEE) publication of 2006 (see reference 10).

A drawback of all these methods about weather conditions is that none of them is able to generate appropriate weather data which are actually to be used to calculate ampacity, which is a value linked to all critical spans of a power lines. A critical span is a span for which there is a significant risk of potential clearance violation in any kind of weather situations. The critical spans of a section may depend on span orientation, local screening effects, local obstacles (vegetation, buildings, roads, . . . ), etc. They have been defined at the design stage but may be reviewed by more modern techniques like Light Detection And Ranging (LIDAR) survey.

The wind speed has a dramatic impact on power line ampacity as it is the main variable responsible for cooling down the conductor, and hence for the sag value.

But wind speed measurement is tricky for various reasons. First, it is not stationary as wind speed can vary significantly within minutes, and there may be wind gusts. Second, it also varies along the span (spatial coherence): wind vortices have a typical average size of several tens of meters (Simiu & Scanlan, 1996). Therefore, a typical span length of several hundreds of meters is subject to a variable wind speed along its length. Third, the wind speed also varies greatly vertically, as the conductor is fastened within the boundary layer, and as the span's lowest point is generally about 10 meters over the ground. The wind speed may also vary due to local effects, such as screening from trees or buildings, altitude of the conductor which may change in a single span of more than 15 meters if only the sag is considered, but which may also be subject to difference of levels between end points of a span. Such a difference in altitude near the ground may have huge effects as the conductor lies in an air layer located in the boundary conditions of wind speed variation due to the ground proximity.

Therefore, a single-spot measurement does not allow computing the global effect of the wind over the whole span.

All of these factors are particularly important for low wind speeds (typically for wind speeds component perpendicular to the conductor axis lower than 3 m/s) which are dramatic for ampacity determination. Similarly, a single-spot measurement of “effective incident radiation” does not allow computing the global effect of the combined effect of sun and albedo over the whole span.

Given the importance of power line monitoring, several devices have been proposed to measure at least some of the relevant parameters. For example, it is known that displacement measurement systems placed at a given short distance (e.g. 89 mm) from a cable suspension point (EPRI, 2009) can measure high-frequency vibrations. However, this is only a partial solution to the monitoring problem and such systems are solely oriented to evaluate the life time of power line conductor due to the bending fatigue induced by Aeolian vibrations cycles on conductor strands near clamps.

A number of different methods which perform sag measurement are also known. An example of tentative sag measurement consists in the optical detection of a target clamped on the monitored conductor by a camera fixed to a pylon (U.S. Pat. No. 6,205,867). Other examples of such methods include measurement of the conductor temperature or tension or inclination of the span. A conductor replica is sometimes attached to the tower to catch an assimilated conductor temperature without Joule effect. Beside the fact that they only allow a partial monitoring of the power line, all of these methods suffer from drawbacks: optical techniques are sensitive to reductions of the visibility induced by meteorological conditions while the other measurement methods are inaccurate, since sag has to be deduced by algorithms which depend on unavailable and/or uncertain data (e.g. wind speeds, topological data, actual conductor characteristics, . . . ) and/or uncertain models.

U.S. Pat. Nos. 5,140,257 and 5,341,088 disclose a monitoring device whose housing is attached to the conductor. Some features are related to the measurement of wind speed and direction based on hot wire anemometers. The drawback of this device is that hot wires anemometer is extremely difficult to manage on a sensor attached to a conductor. Moreover, wind speed is deformed by the sensor itself as hot wire needs to be protected against corona.

U.S. Pat. Nos. 6,441,603 and 5,559,430 disclose a monitoring device for overhead power line rating but not attached to the conductor. It is a kind of conductor replica. The combined effect of wind, solar radiation, albedo, ambient temperature evaluation is based on the behavior of dedicated rods installed apart from the line. Drawback of such method is that the effect along the span was not taken into account and that such local measurement is not a good indication of what is actually the mean wind speed and global incident radiation along spans of several hundreds of meters with possible variable altitudes and different kind of wind action along the span. Moreover, there are obvious errors for replica compared to conductor emissivity and absorptivity and global incident radiation mean value along the span.

U.S. Pat. No. 4,728,887 discloses a monitoring device whose housing is adjacent to the overhead line. There is no information about how wind speed and its direction are taken into account to evaluate ampacity.

U.S. Pat. No. 5,933,355 discloses software to evaluate ampacity of power line. This has no relationship with wind speed measurement.

U.S. Pat. No. 6,205,867 discloses a power line sag monitor based on inclination measurement. There is no information about how wind speed and direction are taken into account to calculate ampacity.

PCT Application WO 2010/054072 is related to real time power line rating. It alleged the existence of a sensor about wind speed direction and amplitude but offered no explanation how these sensors are constituted.

PCT Application WO 2004/038891 and Norway Application N020024833 disclose a monitoring device whose housing is attached to the conductor. The wind is measured by “a traditional wind gauge” and that such wind gauge “operates with an opening in the outer casing”. Such traditional gauge has no relationship with the proposal of the inventors. The drawback of such traditional gauge is that the sensor itself constitutes a perturbation in the local measurement and that low wind speed cannot be measured properly by such gauge.

European Patent Application EP 1.574.822 discloses a monitoring device whose housing is attached to the conductor. There is no information about how wind speed and direction are taken into account to evaluate ampacity.

Korean Patent Application KR20090050671 discloses a monitoring device whose housing is attached to the conductor. A drawback of this device is that there is no way to properly determine the “effective wind speed” perpendicular to the conductor if they are less than 3 m/s, which are the basic cases for ampacity determination under critical conditions.

U.S. Patent Application Publication No. US 20120029871 A1 discloses a monitoring device whose housing is attached to the conductor. A drawback of this device is that there is no explanation on how to evaluate the wind speed to consider for ampacity determination. There is neither description nor any patent on use about wind speed evaluation for ampacity determination. On a website of that system, it is stated that “We also tasked the sensors to detect Aeolian vibration, which is an indication of wind blowing across the conductor, and ‘galloping.’ “(extracted from http://www.lindsey-usa.com/newProduct.php). But there is no explanation on how such link is done. It is well known from the literature that Aeolian vibration frequencies are linked to wind speed (see references 6, 8 and 9). However, there is no mention in the literature to exploit such link in evaluating precisely the acting wind speed on a power line span to compute the ampacity of that line. To do so, it needs the precise determination by an appropriate system of the Aeolian vibration periods with their acting main frequency, which is detailed in this invention by the inventors.

SUMMARY OF THE INVENTION

The present invention meets a need for a power line device and method overcoming at least some of the problems left open by prior art solutions. The present invention is based on a power line sensor directly fixed on the power line conductor (or one of it in case of bundle conductors) and equipped with accelerometers outputs in several directions. The present invention will use redundant information made available in all or part by these accelerometers.

An object of the present invention is to provide a method to measure “effective wind speed” acting on a power line span by using the combination of mechanical vibrations and movements/positions in two or three dimensions outputs through sensors in direct link with the power line conductor.

Another object of the present invention is also to provide a method to determine indirectly an “effective incident radiation” acting on a power line span by using the combination of mechanical vibrations and movements/positions in two or three dimensions outputs through sensors in direct link with the power line conductor.

The sensor must be located at any in-span position. The device used to detect vibration may be based (but not necessarily) on U.S. Pat. No. 8,184,015, in which the device was used in the harsh environment constituted by the vicinity of a high voltage (tens to hundreds of kV) overhead power line.

The sensor must be equipped with accelerometers of significant sensitivity, typically able to detect accelerations near about maximum 100 micro-G in vertical, (longitudinal) and transversal directions (means minimum 2D, possibly 3D accelerometers).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram showing how the wind is acting on conductor including wind effect and mean swing angle θ of power line span, wherein “transversal swing angle” is defined as tan(θ).

FIGS. 2 a and 2 b show the sag as deduced by oscillation sensor outputs (with its maximum value) (FIG. 2 a) and deduced conductor temperature (FIG. 2 b) together with ambient temperature (here measured in the vicinity of the power line span) during a one day time evolution. In FIG. 2 a, sag is deduced by an oscillation sensor from U.S. Pat. No. 8,184,015 (with its maximum allowable value in dotted line). In FIG. 2 b, the thin line represents deduced conductor temperature, and the dotted line represents ambient temperature (here measured in the vicinity of the power line span).

FIGS. 3 a and 3 b show , on the same day, the deduced “effective incident radiation” power as detailed in the invention (FIG. 3 a) and the load current (bottom curve), the static rating (horizontal dotted line at 850 A) and the dynamic rating (thick line) as deduced from effective three weather data, two of them being determined by the invention (FIG. 3 b).

FIGS. 4 a and 4 b show, on the same day, the frequency detection as obtained by using the accelerometers detailed in the invention and tracking of Aeolian periods. FIG. 4 a is a simultaneous view of typical time evolution of detected vibration frequencies and corresponding reinforced Aeolian period vibration frequency tracking according to the invention. FIG. 4 b shows extracted Aeolian vibration tracking as detailed in the invention. Missing data around 12:00 during about 4 hours are due to the absence of detected Aeolian vibration during the corresponding period.

FIGS. 5 a and 5 b show, on the same day at time 12:00, the frequency-amplitude content of the measured signal by the accelerometers detailed in the invention. The typical frequency of “Type I” (buffeting) content as can be extracted from FIGS. 4 a and 4 b (reproduced in FIG. 5 a) at measurement time of about 12:00 (vertical dotted line on the frequency-time figure).

FIGS. 6 a and 6 b show, on the same day at time 04:30, the frequency-amplitude content of the measured signal by the accelerometers detailed in the invention. Typical frequency of “Type II” (Aeolian vibrations) as can be extracted from FIGS. 4 a and 4 b (reproduced in FIG. 6 a) at measurement time of about 04:30 (vertical dotted line on the frequency-time figure).

FIG. 7 shows the values of power line conductor “transversal swing angle” as obtained using the accelerometer-based method detailed in the invention. Swing angle (radians) of the power line span (in this case a conductor of about 0.257 kg/m and a diameter of 12.5 mm) during the same day of observation as for FIGS. 2 to 6. The value is extracted from transversal acceleration of the embedded corresponding accelerometer into the in-span power line sensor. For about 3 m/s wind speed, the mean swing angle is about 0.025 rd or 1.4°. Values below about 0.0025 radian are below the expected precision of the system and cannot be considered for use.

FIG. 8 shows the “effective wind speed” during the same day, as calculated according to the present invention. In this case, the thick black part of the curve has been fully deduced from actually observed Aeolian vibrations in a range limited to wind speed lower than about 1.6 m/s (larger range are also possible). The curve has been completed for larger wind speed, by the thick grey part of the curve deduced from transversal acceleration analysis as detailed in the invention. The typical continuous wind speed value obtained as detailed in the invention. Wind speed deduced by combining Aeolian vibration tracking and transversal acceleration analysis. The thick black line represents wind speed deduced from Aeolian vibrations during such periods, as deduced from FIG. 4 using the invention. The thin cross line represents wind speed deduced from mean transversal acceleration, as deduced from FIG. 7 using the invention.

FIGS. 9 a-9 d show a typical time evolution on 10 minutes of vertical and horizontal accelerations (Type I) during a buffeting period. FIGS. 9 a and 9 c show transversal accelerations. FIGS. 9 b and 9 d show vertical accelerations. The range of relative changes are similar in both directions.

FIGS. 10 a and 10 b show a typical growing up and decay of Aeolian vibrations (Type II) of about 10 minutes inside a global observation period of 50 minutes. FIG. 10 a shows transversal accelerations and FIG. 10 b shows vertical accelerations. Range of relative changes are very different with a clear dominance in vertical amplitudes.

DETAILED DESCRIPTION OF THE INVENTION

The new method according to the present invention adds, in parallel with the thermal equilibrium equation (as described in detail, for example, in IEEE 2006 and reproduced in pages 15 to 17), a second independent equation to determine the most changeable (both in time and space) and most important weather variable for ampacity determination: the wind speed perpendicular component to the conductor axis averaged over the whole span, so called “effective wind speed”.

The required wind speed for ampacity determination is evaluated independently from the thermal equation by means of two independent methods (the results of which are being superimposed or complemented in some range of detected wind speeds). Those two methods determine the wind speed perpendicular component averaged over the span:

-   -   (1) The measurement of the frequency of the Aeolian vibration         that is linked to the wind speed perpendicular component via the         well documented Strouhal equation. Aeolian vibrations may be         active on all the range of wind speeds of interest for ampacity         calculation and are particularly useful in the very low wind         speed range, from near 0 m/s to a few m/s, most preferably         between 0.1 and 3 m/s.     -   (2) The span “transversal swing angle” that, according to the         measurement of the present invention (owing to transversal         acceleration sensor), has shown to be a good indicator of wind         speed perpendicular components exceeding about 1 m/s. For a         one-span section, the cooling effect of the wind speed         perpendicular component is always very close to the one         resulting from the “effective wind speed”, for actual winds         blowing with angles to the conductor axis ranging between 45°         and 90°. Considering wind speed perpendicular component in         calculations thus yield a very good estimate of the ampacity in         that case. For angles ranging from 0° to 45°, the cooling effect         of the wind speed perpendicular component is always inferior to         the one resulting from the “effective wind speed”, thus leading         to a conservative ampacity calculation.

For a multiple-span section, a sensor has to be repeated on all critical spans along the section and the worst case is considered for ampacity evaluation.

A three-axis accelerometer assembly with a range of frequency comprised between 0 and about 100 Hz and a minimum sensitivity of 100 micro-G may detect ambient Aeolian vibrations, often existing at very low wind speed, preferably, comprised between 0.05 and about 7 m/s and, most preferably, between 0.2 and 3 m/s. The accelerometers are able to detect basic oscillation modes of the power line. It is noted here that only the detection of Aeolian vibration frequency is needed. The vibration could be of very low amplitude. An observed Aeolian vibration is obviously linked to a lock-in (as detailed in EPRI 2009) of the vortex shedding with one mode (sometimes a few modes in a very narrow band of frequencies) of vibration of the cable. That detectable frequency(ies) by the line monitoring device is the driving mode or the converted energy from the wind to the vibration in its dominant mode all over the span. Thus, it is representative of the dominant mean wind speed to consider all along the span for thermal convection heat exchange.

The “effective wind speed” for power line span may be deduced from vibrations analysis. This method is particularly valuable for very low wind speed, lower than about 7 m/s, most preferably lower than 3 m/s, which are the dramatic cases for ampacity determination.

It is known from fluid mechanics (Blevins1990, Simiu et al, 1996) that the peaks of power spectral density of oscillations (preferably comprised between 3 and 100 Hz and most preferably between 2 and 40 Hz) is observed at frequencies related to the wind speed and the conductor diameter by the Strouhal relationship, so that a given wind speed will generate vibrations in a close range of frequencies and vice-versa. The observed frequencies are an image of the actual wind speed component perpendicular to the conductor axis as observed in Godard, 2011. Detailed literature exists on that subject as Aeolian vibration is a key phenomenon in connection with the fatigue of the conductors (EPRI 2009). But the phenomenon is used in a another way in the present invention, using observed vibration frequencies to evaluate the speed of wind acting on the span and in turn use such wind speed to compute ampacity of the line.

Appropriate algorithm has been developed by the inventors to extract period of Aeolian vibrations inside the global frequency spectrum. This method is based on the following two steps:

-   -   (1) Step 1: Detection of conductor accelerations ranging from         near 0 Hz to a few tens of Hertz, most preferably between 0 and         about 15 Hz. This last upper value of observation is linked to         conductor diameter and range of wind speed to be detected         following the Strouhal relationship (with S=0.185 or close to         that value). For example to detect wind speed from near 0 m/s to         2 m/s on a conductor diameter of 30 mm (=0.03 m), range of         frequencies to be observed should be near 0 to 12.3 Hz         (12.3=2×0.185/0.03). Sensitivity of accelerometer(s) must be         most preferably close to or better than 100 micro-G. The         quasi-vertical movement (based on normalized amplitudes of the         accelerations sample in each direction) is detected.         Observations period sample needed to perform the frequency         analysis is near a few minutes, most preferably between 2 and 5         minutes. A typical output of such detection is shown on FIG. 4.     -   (2) Step 2: Detection of Aeolian vibration pattern and its major         frequency component, into the general frequency spectrum deduced         from step 1. The acceleration spectrum, as shown on FIG. 4, can         be divided into three main classes of frequency spectrum shapes         and corresponding periods of movements.         -   (2.1) Type I: buffeting             -   Buffeting pattern, as shown on FIG. 5 for the period of                 observation near 12:00, mainly relates to random and                 irregular effects due to variation of wind speed both in                 module and direction along the span. Such power line                 span excitation does not allow the formation of                 “quasi-stationary” vibrations. This causes random                 excitation of the conductor over a broad range of                 frequencies and corresponding vibrations modes                 simultaneously. A large number of modes are present due                 to the spatial/temporal non uniformity of wind. A                 typical time evolution during 10 minutes is given on                 FIG. 9 (accelerations).         -   (2.2) Type II: Aeolian vibrations             -   As shown on FIG. 6 (extracted from FIG. 4 at near 04:30                 time, but also valid for the whole period of observation                 between 00:00 and about 11:00) a very limited number of                 (medium to high, in this case between 3 and 15 Hz)                 frequencies are excited.             -   On the other hand, lower range of vibrations modes with                 frequency lower than Strouhal frequency corresponding to                 very low or low wind speeds (typically near 0.2 m/s),                 are not excited. This frequency threshold is given by                 Strouhal equation and depends on conductor diameter. For                 a conductor with diameter of 30 mm this “lower range”                 limit is typically near 1.2 Hz.(=0.2×0.185/0.03                 following the Strouhal relationship).             -   For a given cylinder diameter and given fluid velocity,                 the shedding frequency of the flow is given by the                 Strouhal equation. For a real conductor, the problem is                 complicated both by the fact that the conductor does not                 behave as a rigid cylinder and the wind speed is a                 function of time and space (wind speed is changing not                 only in time but also along the span with its spatial                 coherence). So some close frequencies are excited and                 thus beat with each other. The frequency component with                 highest normalized displacement amplitude is considered                 here.             -   An Aeolian vibration is characterized to be a more or                 less stationary process in frequency domain, but not                 necessarily in amplitude. Correlation between the                 frequency content of a few successive periods of                 analysis is checked. The positive correlation                 coefficient must be over about 0.9. In others words, an                 Aeolian vibrations period corresponds to a series of                 successive correlated periods of analysis with very                 limited number, typically about 3 close values, of                 medium or high frequencies.             -   Additional information used to detect Aeolian vibration                 is the ratio of vertical to transversal amplitudes of                 vibrations analysis. During buffeting, gusts put the                 conductor in motion, in both vertical and transversal                 directions. During Aeolian vibration, conductor motion                 is mainly perpendicular to the flow, i.e vibrations                 mainly occurs in the vertical plane for power Lines as                 the flows mainly blows horizontally on a flat terrain.                 The mainly vertical resultant oscillation in case of                 Aeolian vibrations is resonant (a very narrow band of                 frequencies are excited). A ratio near 10 is observed                 between vertical and transversal movement.             -   A typical time evolution of Aeolian vibrations is shown                 on FIG. 10.     -   (2.3) Type III: transition period     -   It is a period of transition from type I to type II (or vice         versa) class as defined hereinabove. During the transition from         Type I to Type II, low-frequency amplitudes (For a 30 mm         diameter conductor, this “lower range” limit is typically near         0.2×0.185/0.03=1.2 Hz, following the Strouhal relationship)         decrease and the medium to high frequency amplitudes increase.         Aeolian vibration is building up. When the Aeolian vibration is         built up the conductor is vibrating with a frequency         corresponding to the wind velocity given by Strouhal equation.         The frequency of vibration will not change when the velocity is         changing slightly owing to the well-known (EPRI 2009;         Blevins 1990) lock-in phenomenon: only the vibration amplitude         will decrease but if the wind speed changes too much, the         Aeolian vibration will die (transition to buffeting period) or a         new Aeolian vibration at a new main frequency will build up.         Such a transition period can last a few minutes, typically         between about 2 and about 5 minutes.     -   Observing amplitudes trends of excited frequencies on a given         period allows characterizing transition period.

Determination of the “Effective Wind Speed”

The observed established Aeolian vibration is directly linked to the wind speed and conductor diameter as given by the Strouhal relationship:

f=S·V/d   (1)

where f is the frequency of vibration (Hz) as extracted from step 2, S is the Strouhal number (dimensionless), V is the perpendicular wind speed (m/s), d is the conductor diameter (m). The Strouhal number, for typical power line conductor is close to 0.185 and is dimensionless. (See Blevins 1990, Simiu et al., 1996, EPRI 2009).

FIG. 8 shows a typical output of “effective wind speed” using Aeolian vibration detection algorithm. In this case (one full day), the values have been completed by some transversal inclination (also obtained by accelerometers) during high wind speed periods.

The power line span swing angle (shown in FIG. 1) can be evaluated by considering the equilibrium per unit length between the weight of the conductor and the drag force F_(D) of wind. Hereinbelow, “transversal swing angle” is referred to as tan(Θ) where (Θ) is the mean swing angle of the power line span, see FIG. 1.

The following equation is obtained.

$\begin{matrix} {{\tan (\vartheta)} = \frac{F_{D}}{\rho \; g}} & (2) \end{matrix}$

where ρ is the linear density of conductor [kg/m] and g is the gravity constant [9.81 m/s² on earth].

Resulting drag force F_(D) generated by wind is related to wind speed U [m/s] by the well-known equation (see references 7, 8 or 9):

$\begin{matrix} {F_{D} = {\frac{1}{2}\rho_{air}C_{D}d\; U^{2}}} & (3) \end{matrix}$

Where d [m] is the diameter of the conductor, ρ_(air) the air density [kg/m³] and C_(D) the drag coefficient [dimensionless].

The two previous equations show that the “transversal swing angle” of conductor is linearly related to the square of wind speed, depending on some constants.

As can be seen on FIG. 1, “transversal swing angle” is also given by inclination of transversal axis t with gravity g, that value may be extracted from embedded accelerometers into the sensor installed on the power line conductor:

$\begin{matrix} {{\tan (\vartheta)} = {\frac{{transversal}\mspace{14mu} {static}\mspace{14mu} {acceleration}}{{gravity}\mspace{14mu} {constant}} = \frac{g_{t}}{g}}} & (4) \end{matrix}$

By combining previous equations, wind speed can be determined, using transversal acceleration g_(t) [m/s²].

$\begin{matrix} {U^{2} = {{\frac{\rho}{0.5\rho_{air}C_{D}d}g_{t}} = {k_{i} \cdot g_{t}}}} & (5) \end{matrix}$

As an example, the following values could be used: (i) the air density r_(air)=1.2 kg/m³ at 20° C. (ii), the drag coefficient C_(D)=1. This means that, for a conductor with diameter of 0.03 m and a linear density of 1 [kg/m], equation (5) gives an approximated relationship between wind speed and static transversal acceleration given by U²=55 g_(t) (means in this case k_(i)=55 m).

In real cases, dynamic motion in transversal direction is induced by wind gusts and transversal acceleration can change rapidly. Mean value of transversal acceleration is measured to evaluate mean wind speed acting on the conductor. That mean value is obtained on sample size range from about 5 to 20 minutes, most preferably around 10 minutes mean value is used.

Choosing accelerometers of sensitivity better than 100 micro-G, it is possible to get transversal inclination values once the wind speed is still in the range of Aeolian vibration, which gives a self-calibration (=find the “k_(i)” value) of the linear relationship between transversal inclination and the square of the wind speed, as shown on FIG. 7. Obviously, when there is no wind, inclination must be zero, which gives an obvious starting point of the linear fit. Initial offset of inclination, if any, may be determined by that method.

Determination of the Worst Weather Conditions Acting on the Power Line, in Particular the “Effective Incident Radiation”

Based on the new method, one can determine the effective worst weather conditions needed to compute the real-time thermal rating (also called dynamic line rating—DLR—or real time thermal rating—RTTR—) (shown on FIG. 3, right upper curve) of the overhead line in three steps:

1. Effective perpendicular wind speed (“effective wind speed”), the variable with the most influence on the RTTR/DLR is determined as described above: at low wind speeds using the Aeolian vibration and at higher wind speeds, if needed, using the “transversal swing angle” (FIG. 1).

2. Ambient temperature (shown on FIG. 2, right bottom curve) is determined based on an external or internal measurement in the monitoring sensor or located in general vicinity of the line. As ambient temperature varies little (compared to the other variables) over time, distance or altitude, a measurement performed even several kilometers away from the overhead line may be adequate.

3. The “effective incident radiation” (comprising direct solar radiation and environment's albedo along the span) (FIG. 3 a) is determined by using the sag measurement (FIG. 2 b, upper curve)(which may be also obtained by accelerometers as explained in U.S. Pat. No. 8,184,015 which allows for calculating the sag without any external data) as follows:

This is done by using thermal equilibrium equation (as detailed in IEEE 2006 and reproduced in appendix) and will need the load current in the line (FIG. 3 right bottom)(deduced from load flow in the line which is either transmitted by the TSO or directly measured into a sensor installed on the power line) to quantify the Joule effect, the “effective wind speed” (determined in step 1), ambient temperature (determined in step 2), and the conductor average temperature over the span (which is a direct image of the measured sag in a single-span section, as they are bound to each other by a one-to-one relationship as detailed in reference 4); the “effective incident radiation” can then be calculated by solving the thermal equilibrium equation:

q _(s) =q _(c) +q _(r) −R(T _(c)) I ²   (6)

wherein

-   q_(s): heat gain rate per unit length by “effective incident     radiation” (W/m); -   q_(s): convected heat loss rate per unit length by “effective wind     speed” (W/m); -   q_(r): radiated heat loss rate per unit length (W/m); and -   R(T) I²: heat gain rate per unit length by Joule effect (W/m).

The last term being the Joule effect, considering the resistance as a function of the conductor's mean temperature.

The other terms are described below (written here only for forced convection, other formulas to be extracted from ref 2 or 10):

$\begin{matrix} {q_{c\; 1} = {\left\lbrack {1.01 + {0.0372\left( \frac{10^{3}d\; \rho_{f}V}{\mu_{f}} \right)^{0.52}}} \right\rbrack {k_{f}\left( {T_{c} - T_{a}} \right)}}} & (i) \\ {q_{c\; 2} = {\left\lbrack {0.0119\left( \frac{10^{3}d\; \rho_{f}V}{\mu_{f}} \right)^{0.6}} \right\rbrack {k_{f}\left( {T_{c} - T_{a}} \right)}}} & ({ii}) \end{matrix}$

Equation (i) applies at low winds but is incorrect at high wind speeds. Equation (ii) applies at high wind speeds, being incorrect at low wind speeds. At any wind speed, the larger of the two calculated convection heat loss rates is used.

There is a natural convection formula defined in both references 2 and 10, but it is seldom applied, as a minimum wind speed threshold (typically of 0.5 m/s, perpendicular or not) is usually defined by the TSO.

Here the equations are simplified by taking into account that the patent determine the “effective wind speed” which is the perpendicular equivalent wind speed needed.

Thus, there is no more angular coefficient to take into account for the present method.

Radiated heat loss rate

$q_{r} = {0.0178{.10}^{3}d\; {ɛ\left\lbrack {\left( \frac{T_{c} + 273}{100} \right)^{4} - \left( \frac{T_{a} + 273}{100} \right)^{4}} \right\rbrack}}$

This radiation term follows the well-know Stefan-Boltzmann law.

The rate of “effective incident radiation” is then simply deduced by the formula:

q _(s) =q _(c) +q _(r) −R(T _(c)) I ²

This radiation term includes solar heat, if any, and albedo.

The variables used in this appendix are described in the following list:

R(T_(c)): AC resistance of conductor at temperature T_(c)(Ωm)

I: conductor current (A)

d: conductor diameter (m) (typically around 0.03 m)

ρ_(f): density of air (kg/m³) (1.184 kg/m³ at T_(a)=25° C. and altitude=0 m)

V: “effective wind speed” (m/s)

μ_(f): dynamic viscosity of air (Pa·s) (1.84·10⁻⁵ Pa·s at T_(a)=25° C.)

k_(f): thermal conductivity of air (W/(m.° C.)) (0.0261 W/(m.° C.) at T_(a)=25° C.)

T_(c): conductor temperature (° C.)

T_(a): ambient air temperature (° C.)

ε: emissivity (0.23 to 0.91) (dimensionless)

In FIG. 3 a, the “theoretical” sun power deduced from latitude and date (following equations detailed in IEEE, 2006) are given for comparison with actual output from the invention.

This approach, comprising redundant information (two measurements of the “effective wind speed”, plus the sag measurement), allows one to determine RTTR (real time thermal rating) with a precision not yet attained by any of the current methods and tools, as point measurement methods are corrected using the behavior of the overhead line itself and even approximations of the thermal model and its variables (emissivity, humidity for example) are compensated by the correction applied to the “effective incident radiation” using the sag measurement.

Such weather data can be evaluated on all critical spans of the line and help to compute ampacity for each case and select the worst case for the line. “Effective wind speed” can be used for an even broader range of applications, like the determination of the wind dynamic pressure coefficient, or the conductor maximum swing angle, used for line design.

A side outputs of these measurement is the availability of past behavior (in both sag, lateral movement, “effective wind speed”, ampacity, . . . ) including long term behavior.

REFERENCES

-   -   [1] A. Deb. “Power line ampacity system.” 2000. CRC Press (251         pages).     -   [2] “Thermal behaviour of overhead conductors”. 2002. Cigre         Technical brochure No. 207. Study Committee B2.     -   [3] “Guide for selection of weather parameters for bare overhead         conductor ratings”. 2006. Cigre technical Brochure No. 299.Study         Committee B2.     -   [4] “Sag-tension calculation methods for overhead lines”. 2007.         Cigre Technical Brochure No. 324. Study Committee B2.     -   [5] “Guide for application of direct real-time monitoring         systems”. 2012. Cigre Technical brochure No. 498. Study         Committee B2.     -   [6] Godard, B, Guerard, S, & Lilien, J.-L. Original real-time         observations of aeolian vibrations on power-line         conductors. 2011. IEEE Transactions on Power Delivery, 26(4),         2111-2117. http:/lhdl.handle.net/2268/102095     -   [7] Blevins R. D. Flow Induced Vibration. 1990. Van Nostrand         Reinhold, New York, Second Edition.     -   [8] EPRI Transmission line reference book: Wind induced         conductor motion. Second Edition. 2009. EPRI, Palo Alto,         Calif.: 2009. 1018554.     -   [9] Simiu E., Scanlan R. Wind effects on structures. 1996. John         Wiley & Sons, Inc. (688 pages).     -   [10] IEEE Std 738-2006—IEEE Standard for Calculating the         Current-Temperature of Bare Overhead Conductors. IEEE Power         Engineering Society. 2006. 

1. A method for the determination of wind speed to be used for evaluation of the ampacity in using real-time monitoring of at least one span of overhead power lines, comprising the steps of: measuring Aeolian vibration frequency by using outputs of at least one oscillation sensor; and determining wind speed component perpendicular to the conductor axis according to the following equation: V=f·d/S wherein f is the Aeolian vibration frequency (Hz), S is the Strouhal number, V is perpendicular wind speed (m/s), and d is conductor diameter (m).
 2. The method according to claim 1, comprising the steps of: acquiring monitoring information from at least one monitoring device of the power line by using at least one oscillation sensor; performing a frequency or time-frequency analysis from at least one monitoring device of said oscillation measurement signals ranging from 0 to about 100 Hz with a sensitivity of about or more than 100 micro-G for accelerations; determining a fundamental frequency from said frequency or time-frequency analysis; and determining sag of the span, on which at least one monitoring device is clamped.
 3. The method according to claim 2 further comprising the step of determining signature of Aeolian vibrations.
 4. The method according to claim 2 further comprising the step of determining the frequency spectrum partly or totally, including DC component, of a transversal inclination of the overhead line in service in the range of about 0 to mechanical fundamental frequency of the span, the DC component being proportional to the square of the mean wind speed component perpendicular to the power line measured for about 5 minutes, wherein self-calibration of the conversion from inclination to the effective wind speed is obtained owing the recovery range with the same wind speed deduced by Aeolian vibration.
 5. The method according to claim 2, further comprising the determination of effective incident radiation by using the sag of the span, the relationship between sag and conductor temperature, the measured ambient temperature, the electrical current flowing in the line and the effective wind speed.
 6. A device for the determination of wind speed for evaluation of the ampacity in using real-time monitoring of at least one span of overhead power lines, comprising: a sensor for attaching to a conductor of the power line, said sensor comprising an accelerometer; and a processor in connection with the sensor for calculating the wind speed; wherein the processor determining wind speed component perpendicular to the conductor axis according to the following equation: V=f·d/S wherein f is the Aeolian vibration frequency (Hz), S is the Strouhal number, V is perpendicular wind speed (m/s), and d is conductor diameter (m).
 7. The device according to claim 6, wherein the sensor is an oscillation sensor measuring Aeolian vibration frequency.
 8. The device according to claim 6, wherein the accelerometer is able to detect accelerations about maximum 100 micro-G in a vertical direction and a transversal direction.
 9. The device according to claim 6, wherein the accelerometer is able to measure acceleration in three-dimensional directions. 